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The following is an instructable on making a wooden ring out of teak at Techshop RDU. These rings can be made out of any hardwood, but teak is both water resistant and strong enough to remain intact, even with a slender profile.
Take a look at the Etsy.com website I just put up:
I started with a 3/4" forstner bit. Pick out a size that is good for you. If it's a little too small, you can sand it open further in the production process.
Square up the bit and drill as close to the center of your piece as possible. It's not a bad idea to drill a few extra pieces while you're at it. Can't hurt.
Next, we head over to the bandsaw to do some rough cuts. Round out the edges somewhat before the next step. (Safety First: wear glasses and take your time on the bandsaw)
Here is an example of a ring roughed out and prepared for further sanding on the belt sander.
Belt sanding is broken down into two separate steps:
1) Even out the thickness of the ring on all sides. It doesn't have to be exact, as you'll come back later, but the closer you get it here the less hand sanding you have to do.
2) Tilt the ring slightly to the side, first one way and then the other, in order to round the edges off. After this step it'll begin to look less like a scrap piece and more like an actual ring. The rounding allows to to taper the profile while maintaining most of the rings structrual stability.
Next is the oscillating sander with the smallest available sanding pad (and something around 80 grit). If you dont have the machine you can also hand file, which takes longer but allows you more control. Take the ring out repeatedly at this point and try it on to make sure it hasn't loosened too far.